Pell number

The Pell sequence is a mathematical sequence of positive integers, the Pell numbers (English Pell numbers ), as well as the Pell numbers 2 (ger companion Pell numbers ). It takes its name from the English mathematician John Pell ( 1611-1685 ).

Pell sequence / numbers

The sequence is defined recursively by:

This means in words:

• For the first two numbers, the values ​​zero and one are given
• Any other number is calculated by doubling the direct predecessor and subsequent addition of the pre-predecessor.

The first numbers of the sequence are 0, 1, 2, 5, 12, 29, 70, 169, 408, ... ( sequence A000129 in OEIS )

The Pell sequence can also be as a special case of the general Lucas sequence Un ( P, Q) with P = 2 and Q = -1 interpret:

Pell numbers 2 Art / Companion Pell sequence

Pell numbers second kind are also called Pell -Lucas numbers.

The sequence is defined recursively by:

This means in words:

• For the first two figures of the value two is given
• Any other number is calculated by doubling the direct predecessor and subsequent addition of the pre-predecessor.

The first numbers of the sequence be 2, 2, 6, 14, 34, 82, 198, 478, 1154, ... ( sequence A002203 in OEIS )

The Companion Pell sequence can also be as a special case of the general Lucas sequence Vn (P, Q) with P = 2 and Q = -1 interpret:

• Sequences and series